This section is intended to introduce various aspects of the art, which may be associated with exemplary embodiments of the present invention. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the present invention. Accordingly, it should be understood that this section should be read in this light, and not necessarily as admissions of prior art.
Many applications involve processing information about physical properties. When processing information relating to physical properties of complex systems, it may be desirable to provide a physical property model representative of physical properties that are useful for a specific purpose. In the field of hydrocarbon exploration, examples of properties that may be useful include resistivity and seismic impedance. These properties may help hydrocarbon exploration professionals to locate hydrocarbon resources in the subsurface of the earth or to improve production of known hydrocarbon resources.
One example of information processing is the transformation of information residing in a first domain into information residing in a second domain. Such a transformation may be desirable because, for example, acquired or measured information may inherently reside in a first domain, such as a data domain. When expressed in the data domain, the information may not be directly useful for a desired purpose such as hydrocarbon exploration. By transforming the information residing in the data domain into a second domain, such as a model domain, the information may be more useful for the desired purpose. The information in the model domain may comprise a physical property model representative of a physical property of interest.
FIG. 1 is a block diagram that is useful in explaining the improvement of the accuracy of a physical property model in a model domain through one or more cycles of forward modeling and model updates. The diagram is generally referred to by a reference number 100. A model domain 102 comprises information that describes one or more physical properties of a region. The physical properties described in the model domain may be useful for performing tasks such as hydrocarbon exploration. For example, the model domain 102 may comprise information that describes controlled source electromagnetic (CSEM) properties such as resistivity and/or seismic properties such as seismic impedance.
One known technique for gaining relevant information about subsurface regions employs a forward modeling process 104 to transform information from the model domain 102 into a data domain 106. The data domain 106 comprises data obtained from actual observation and may also include modeled or simulated data created by the forward modeling process 104.
To improve the predictive capability of information in the model domain 102, simulated data created by the forward modeling process 104 may be compared to actual observed data in the data domain 106. Differences or misfit between the simulated data created by the forward modeling process 104 may be used to make adjustments to the corresponding information in the model domain 102 so that subsequent iterations of the forward modeling process 104 produce simulated data that more closely matches actual known or observed data. When the misfit is small for simulated data for which corresponding known or observed data exists, the accuracy of simulated data for which no corresponding known or observed data exists may be assumed.
Data in the data domain 106 may be transformed into information in the model domain 102 through a model update process 108. Moreover, the accuracy of information in the model domain 102 may be systematically improved by iteratively performing the steps of transforming information from the model domain 102 into simulated data in the data domain 106 via the forward modeling process 104, comparing the misfit of known data values with the simulated data in the data domain, then performing the model update process 108 to adjust the model domain property values.
Information in the model domain 102 may also be transformed into a derived model 112 through the use of a rock physics evaluation process 110. Examples of properties that may be expressed as derived models 112 include lithology, fluid type, saturation or the like. The model update process 108 typically involves the use of very large amounts of data from the data domain 106. Because of the scope of the amount of data that is used, current practices provide only a single global or average data misfit or error for an entire iteration of the model update process 108.
FIG. 2 is graph that is useful in explaining a known technique of using a global or average error to improve the accuracy of a physical property model. The graph is generally referred to by the reference number 200. A y-axis 202 is a logarithmic scale showing misfit between simulated data produced by the forward modeling process 104 relative to known data in the data domain 106. An x-axis 204 shows a number of iterations of performing the forward modeling process 104. A trace 206 shows a significant decrease in average misfit through a first inversion round of about 12 iterations. Toward the end of the first inversion round, the reduction in misfit slows, which may be taken as in indication that further significant reduction in average misfit is unlikely given the information in the model domain 102. At the end of the first inversion round, the information in the model domain 102 may be adjusted prior to beginning a second inversion round.
A trace 208 shows that average misfit is initially improved for the second inversion round relative to the start of the first inversion round. The reduction of average misfit does not, however, decline as dramatically during the second inversion round. A decline in the rate of average misfit improvement after about 17 iterations indicates that significant reduction in average misfit is unlikely based on the current information in the model domain 102. After the second inversion round is completed, the information in the model domain 102 may again be adjusted prior to beginning a third inversion round.
A trace 210 shows that average misfit is initially improved for the third inversion round relative to the start of the second inversion round. A decline in the rate of average misfit improvement after about 25 iterations indicates that significant reduction in average misfit is unlikely to continue based on the current information in the model domain 102. At the end of the third inversion round, it may be determined that further improvement in the reduction of misfit is unlikely to justify subsequent rounds of inversion.
FIG. 3 is a graph that shows a degree of misfit between actual data and simulated data for individual data elements. The graph is generally referred to by the reference number 300. The graph 300 is useful in explaining the inherent limitations in using average misfit as a measure of determining whether subsequent rounds of inversion are justifiable.
A y-axis 302 is a logarithmic scale showing a degree of misfit between simulated data produced by the forward modeling process 104 (FIG. 1) relative to known data. An x-axis 304 represents distance in units of meters. A first actual data trace 306a corresponds to an actual data element in the data domain 106 (FIG. 1). The first actual data trace 306a may represent data at 0.25 Hz gathered by a single receiver in a field experiment. A first simulated data trace 308a represents simulated data (also at 0.25 Hz) from the forward modeling process 104 (FIG. 1) that is intended to correspond to the actual data represented by the first actual data trace 306a. Similarly, a second actual data trace 306b corresponds to an actual data element in the data domain 106 (FIG. 1). The second actual data trace 306b may represent data at 2.5 Hz gathered by a single receiver in a field experiment. A second simulated data trace 308b represents simulated data (also at 2.5 Hz) from the forward modeling process 104 (FIG. 1) that is intended to correspond to the actual data represented by the second actual data trace 306b. 
A potential problem in using average misfit to determine the desirability of performing subsequent rounds of inversion is that the average misfit data illustrated in FIG. 2 may be based on thousands of individual elements of data, such as the first actual data trace 306a and the second actual data trace 306b. Moreover, the sheer volume of data elements in the data domain 106 (FIG. 1) may make it impractical to perform an element-by-element analysis of misfit. For the example of CSEM data, a user would need to individually evaluate the misfit for thousands of combinations of source line, receiver and frequency data obtained during a data gathering operation. The evaluation of misfit information in this manner may not be realistically feasible. Thus, average misfit is typically used even though it does not convey detailed information about the quality of the fit on a region by region basis. The use of average misfit makes decisions regarding whether subsequent inversion rounds might significantly reduce the misfit more speculative.
The following example illustrates potential inaccuracies caused by the use of average misfit. A particular set of data elements in the data domain 106 (FIG. 1) may result from defective collection equipment, such as a non-functioning receiver. Using average misfit data to determine whether subsequent refinement of the information in the model domain 102 would be helpful would hide the effect of the data corresponding to the defective collection equipment. Thus, a user could remain unaware of related inaccuracies represented in the model domain 102 (FIG. 1) and/or the data domain 106 (FIG. 1).
There are several known methods of transforming data related to physical property models. U.S. Pat. No. 7,333,893 describes a method for removing effects of shallow resistivity structures in electromagnetic survey data to produce a low frequency resistivity anomaly map, or alternatively imaging resistivity structures at their correct depth levels. The method involves solving Maxwell's electromagnetic field equations by either forward modeling or inversion, and uses at least two survey data sets, one taken at the source frequency selected to penetrate to a target depth, the other a higher frequency that penetrates shallow depths.
U.S. Pat. No. 7,418,350 describes a method and apparatus for estimating a seismic velocity field from seismic data including time-amplitude representations associated with source-receiver locations spaced apart by an offset distance and having a midpoint therebetween. The seismic data may be arranged into common midpoint (CMP) gathers associated with respective CMP locations. A control plane having an edge intersecting a plurality of the CMP locations is defined, an initial velocity field for the control plane is produced, the initial velocity field including a plurality of time-velocity values for each of the CMP locations; and an optimized velocity field for the control plane is produced by adjusting the time-velocity values for each of the CMP locations in response to trends, relative to offset distance, in time values, associated with common seismic events, until said optimized velocity field satisfies a condition.
U.S. Patent Application Publication No. 20060197534 describes a method for enhancing resistive anomalies in electromagnetic geophysical survey data. Scaled values of a measured electromagnetic field parameter are plotted on a depth section at locations related to corresponding source/receiver locations. Scaling is performed relative to a reference signal selected to represent a baseline free of unknown resistive bodies. Scaled values are represented by a color scale in the display, and the color scale may be adjusted to enhance perceived anomalies. The method may be employed in either the frequency domain or the time domain.
U.S. Patent Application Publication No. 20090006053 describes a method for efficient processing of controlled source electromagnetic data, whereby Maxwell's equations are solved by numerical techniques such as finite difference or finite element in three dimensions for each source location and frequency of interest. The Reciprocity Principle is used to reduce the number of computational source positions, and a multi-grid is used for the computational grid to minimize the total number of cells yet properly treat the source singularity, which is essential to satisfying the conditions required for applicability of the Reciprocity Principle. An initial global resistivity model is Fourier interpolated to the computational multi grids. In systems that perform inversion, Fourier prolongation is used to update the global resistivity model based on optimization results from the multi-grids.
International Patent Application Publication No. WO2007145694 describes a method for updating a velocity model for migrating seismic data using migration velocity scans with the objective of building a model that reproduces the same travel times that produced selected optimal images from a scan. For each optimal pick location in the corresponding test velocity model, a corresponding location is determined in the velocity model to be updated, using a criterion that the travel time to the surface for a zero offset ray should be the same. Imaging travel times are then computed from the determined location to various surface locations in the update model, and those times are compared to travel times in the test velocity model from the optimal pick location to the same array of surface locations. The updating process consists of adjusting the model to minimize the travel time differences.
International Patent Application Publication No. WO2008042081 describes a method for reducing the time needed to perform geophysical inversion by using simultaneous encoded sources in the simulation steps of the inversion process. The geophysical survey data are prepared by encoding a group of source gathers, using for each gather a different encoding signature selected from a set of non-equivalent encoding signatures. Then, the encoded gathers are summed by summing all traces corresponding to the same receiver from each gather, resulting in a simultaneous encoded gather. Alternatively, the geophysical data are acquired from simultaneously encoded sources. The simulation steps needed for inversion are then calculated using a particular assumed velocity (or other physical property) model and simultaneously activated encoded sources using the same encoding scheme used on the measured data. The result is an updated physical properties model that may be further updated by additional iterations.
International Patent Application Publication No. WO2008066628 describes a method for organizing computer operations on a system of parallel processors to invert electromagnetic field data from a controlled-source electromagnetic survey of a subsurface region to estimate resistivity structure within the subsurface region. Each data processor in a bank of processors simultaneously solves Maxwell's equations for its assigned geometrical subset of the data volume. Other computer banks are simultaneously doing the same thing for data associated with a different source frequency, position or orientation, providing a ‘fourth dimension’ parallelism, where the fourth dimension requires minimal data passing. A time limit may be set after which all processor calculations are terminated, whether or not convergence has been reached.
Known methods of improving physical property models do not permit efficient comparison of the misfit between simulated data and known data. An improved system and method for providing such an efficient comparison is desirable.